Question

There is a 1 mm thick layer of oil between a flat plate of area $10^{-2} m^2$ and a big plate. How much force is required to move the plate with a velocity of 1.5 cm/s²? The coefficient of viscosity of oil is 1 poise

• A. None of these

Answer 1

Answer: (A)

The force required is 0.015 N, so the correct answer is None of these.

Answer 2

To find the force required to move the plate, we use Newton's law of viscosity:

$F = \eta A \frac{v}{d}$

Where:

• $F$ is the force required.
• $\eta$ is the coefficient of viscosity.
• $A$ is the area of the plate.
• $v$ is the velocity of the plate.
• $d$ is the thickness of the oil layer.

First, convert all quantities to SI units:

• Viscosity: $\eta = 1 \text{ poise} = 0.1 \text{ Pa·s}$
• Area: $A = 10^{-2} \text{ m}^2$
• Velocity: $v = 1.5 \text{ cm/s} = 0.015 \text{ m/s}$
• Thickness: $d = 1 \text{ mm} = 0.001 \text{ m}$

Now, substitute these values into the formula:

$F = 0.1 \text{ Pa·s} \times 10^{-2} \text{ m}^2 \times \frac{0.015 \text{ m/s}}{0.001 \text{ m}}$

$F = 0.1 \times 10^{-2} \times 15 = 0.015 \text{ N}$

The calculated force is $0.015 \text{ N}$.